Pullback attractors for the nonclassical diffusion equations with memory in time-dependent spaces

In this paper, we consider the asymptotic behavior of nonclassical diffusion equations with hereditary memory and time-dependent perturbed parameter on whole space $ \mathbb{R}^n $. Under a general assumption on the memory kernel $ k $, the existence and regularity of time-dependent global attractors are proven using a new analytical technique. It is remarkable that the nonlinearity $ f $ has no restriction on the upper growth.